-6 1 kg 100 cm m v 15µm = kg 1 hr s. Similarly Stokes velocity can be determined for the 25 and 150 µm particles:

Transcription

1 009 Pearon Educaion, Inc., Upper Saddle Rier, NJ. All righ reered. Thi publicaion i proeced by Copyrigh and wrien periion hould be obained fro he publiher prior o any prohibied reproducion, orage in a rerieal ye, or raniion in any for or by any ean, elecronic, echanical, phoocopying, recording, or likewie. For inforaion regarding periion(), wrie o: Righ and Periion Deparen, Pearon Educaion, Inc., Upper Saddle Rier, NJ SOLUTIONS CHAPTER 11 EXERCISES 7. Conider paricle characerized wih a deniy of 1.5 g/c. A 5ºC and 1 a, deerine he erinal eling elociy of paricle falling in air ha are (a) 15, (b) 5, and (c) 150 µ in diaeer. Deerine he Soke eling elociy for each ize paricle uing Equaion 11.. A 5ºC, he icoiy and deniy for air are aued a kg/ hr and g/c, repeciely. For he 15 µ paricle, Soke equaion predic: g ρ- ρ D g 1 kg 100 c ( ) c 1000 g 1 = - kg 1 hr hr µ = i Siilarly Soke elociy can be deerined for he 5 and 150 µ paricle: (5 µ) = / (150 µ) = / 8. Conider a eling chaber o rea a pariculae ladened air rea haing a olueric flow of 1.0 /. Deign a eling chaber o collec paricle 10 µ in diaeer haing a deniy of 1700 kg/. The chaber i o be 1.5 in widh and 1.5 in heigh. (a) How long u he eling chaber be o gie heoreical perfec collecion efficiency? (b) Uing he lengh deerined in par (a), deerine he collecion efficiency for 5 µ paricle wih he ae deniy. Par a. Uing Soke Law, deerine he erinal eling elociy for he 10 µ paricle. g ρ- ρ D kg ( ) ( 10µ ) = = kg 1 hr i hr 600 Soluion Ch 11 July 5,

2 009 Pearon Educaion, Inc., Upper Saddle Rier, NJ. All righ reered. Thi publicaion i proeced by Copyrigh and wrien periion hould be obained fro he publiher prior o any prohibied reproducion, orage in a rerieal ye, or raniion in any for or by any ean, elecronic, echanical, phoocopying, recording, or likewie. For inforaion regarding periion(), wrie o: Righ and Periion Deparen, Pearon Educaion, Inc., Upper Saddle Rier, NJ Sole Equaion 11.5 for he lengh of chaber required for heoreically reoing 100% of he 10 µ paricle. LW η = ( 100) η L = = = W ( 100 ) ( 1.5 ) Wow, longer han a fooball field! Par b. And iilarly for he 5 µ paricle ue Soke Law o deerine he erinal eling elociy. g ρ-ρ D kg ( 5 10 ) ( 5µ ) = = kg 1 hr i hr 600 Ue Equaion 11.5 o deerine he reoal efficiency of he 5 µ paricle. LW η = 100 = 100 = 6% 9. Deign a eling chaber o collec paricle 50 µ in diaeer and 111 lb/f in deniy fro an air rea wih a olueric flow of 8 f /. The cro-ecional area of he quare inle i 9 f. (a) How long u he chaber be o gie heoreical perfec collecion efficiency? (b) Deerine he collecion efficiency for 10 µ paricle wih he ae deniy. Aue he ga rea eperaure i 70ºF uch ha he ga deniy and icoiy are lb/f 5 and1. 10 lb fi, repeciely. Par a. Uing Soke Law, deerine he erinal eling elociy for he 50 µ paricle. Soluion Ch 11 July 5, 008 8

3 009 Pearon Educaion, Inc., Upper Saddle Rier, NJ. All righ reered. Thi publicaion i proeced by Copyrigh and wrien periion hould be obained fro he publiher prior o any prohibied reproducion, orage in a rerieal ye, or raniion in any for or by any ean, elecronic, echanical, phoocopying, recording, or likewie. For inforaion regarding periion(), wrie o: Righ and Periion Deparen, Pearon Educaion, Inc., Upper Saddle Rier, NJ g ρ- ρ D lb.8 f ( ) f 50µ = 0.4 f = -5 lb f i Sole Equaion 11.5 for he lengh of chaber required for heoreically reoing 100% of he 10 µ paricle. LW η = 100 f 8.0 ( 100) η L = = = 6. f 100 f W ( 100 ) 0.4 ( f ) Par b. And iilarly for he 10 µ paricle ue Soke Law o deerine he erinal eling elociy. g ρ- ρ D lb (.8) f ( ) f f ( 50µ ) = = lb f i Ue Equaion 11.5 o deerine he reoal efficiency of he 10 µ paricle. LW f f.0 f f 8.0 η = 100 = 100 = 4% Soluion Ch 11 July 5, 008 8

4 009 Pearon Educaion, Inc., Upper Saddle Rier, NJ. All righ reered. Thi publicaion i proeced by Copyrigh and wrien periion hould be obained fro he publiher prior o any prohibied reproducion, orage in a rerieal ye, or raniion in any for or by any ean, elecronic, echanical, phoocopying, recording, or likewie. For inforaion regarding periion(), wrie o: Righ and Periion Deparen, Pearon Educaion, Inc., Upper Saddle Rier, NJ Proce exhau ga wih a olueric flow rae of 100,000 cf ha conain 5 gr/f of ceen PM i o be reaed wih an ESP. Regulaory requireen dicae ha he oule PM concenraion u be 0.0 gr/f. Aue a plae-o-plae pacing of 10 inche and an applied olage of 15,000 ol. The alle paricle in he ga rea are µ in diaeer and all paricle hae a dielecric conan of 5.5. Eiae (a) he paricle drif elociy and (b) he required collecion plae area o ee regulaion. Aue andard eperaure and preure. (c) Aue plae wih lengh and heigh of 0 f are ued. Eiae he nuber of plae required. Par a. Knowing he dielecric conan for he du, calculae he conan P. κ 5.5 P = = =. κ Ue Equaion 11.7 o eiae he drif elociy for µ paricle kV 1 ω = E dp P = ,000 V 1000 V 5 in. µ. f ω = 0. Par b. Ue he Deuch-Anderon Equaion 11.6 o deerine he required collecor plae urface area. Fir, deerine he required reoal efficiency uing Equaion 11.. PM - PM gr f ( 5-0.0) in ou η = = = or 99.6% PM gr in 5 f Coner uni for he olueric flow rae: f 1 in f = 100,000 = 1,667 in 60 Sole he Deuch-Anderon Equaion for collecor area, A η = 1- exp - Aω Soluion Ch 11 July 5,

5 009 Pearon Educaion, Inc., Upper Saddle Rier, NJ. All righ reered. Thi publicaion i proeced by Copyrigh and wrien periion hould be obained fro he publiher prior o any prohibied reproducion, orage in a rerieal ye, or raniion in any for or by any ean, elecronic, echanical, phoocopying, recording, or likewie. For inforaion regarding periion(), wrie o: Righ and Periion Deparen, Pearon Educaion, Inc., Upper Saddle Rier, NJ f -1,667 - A = ln ( 1- η ) = ln ( ) ω f 0. A = 7,900f of collecion area required If a plae lengh of 0 f wih heigh of 0 f were ued, he plae area can be calculaed. Recognize ha boh ide of he plae are uilized a collecor. Plae Collecion Area = A plae To deerine he nuber of plae required: A nuber of plae required - 1 = A = 0f 0f = 1,800 f plae 7,900 f nuber of plae required - 1 = f 1800 plae approxiae nuber of plae needed = 17 Soluion Ch 11 July 5,